Comptes Rendus
Damping efficiency of the Tchamwa–Wielgosz explicit dissipative scheme under instantaneous loading conditions
[Efficacité amortissante du schéma explicite dissipatif de Tchamwa–Wielgosz pour des chargements impulsionnels]
Comptes Rendus. Mécanique, Volume 337 (2009) no. 11-12, pp. 722-732.

To deal with dynamic and wave propagation problems, dissipative methods are often used to reduce the effects of the spurious oscillations induced by the spatial and time discretization procedures. Among the many dissipative methods available, the Tchamwa–Wielgosz (TW) explicit scheme is particularly useful because it damps out the spurious oscillations occurring in the highest frequency domain. The theoretical study performed here shows that the TW scheme is decentered to the right, and that the damping can be attributed to a nodal displacement perturbation. The FEM study carried out using instantaneous 1-D and 3-D compression loads shows that it is useful to display the damping versus the number of time steps in order to obtain a constant damping efficiency whatever the size of element used for the regular meshing. A study on the responses obtained with irregular meshes shows that the TW scheme is only slightly sensitive to the spatial discretization procedure used.

Dans le cadre de problèmes de dynamique ou de propagation d'ondes, l'utilisation d'une méthode dissipative est souvent nécessaire pour réduire les oscillations parasites provenant des discrétisations spatiales et temporelles. Parmi les nombreuses méthodes existantes, le schéma explicite dissipatif de Tchamwa–Wielgosz amortit ces oscillations en ciblant son amortissement sur l'énergie des hautes fréquences. Une étude théorique montre ici le décentrage à droite de ce schéma et interprète son amortissement comme une perturbation des déplacements nodaux. L'étude FEM sur des cas de compression impulsionnelle 1-D et 3-D montre l'utilité d'afficher l'amortissement en fonction du nombre de pas de temps et permet d'obtenir une efficacité amortissante constante quelque soit la taille de l'élément utilisé dans le maillage régulier. L'étude de la réponse obtenue pour des maillages irréguliers montre la légère sensibilité de l'amortissement du schéma de TW à la discrétisation spatiale utilisée.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2009.10.005
Keywords: Dynamical systems, Structural dynamics, Explicit and dissipative time integration algorithm, Tchamwa–Wielgosz scheme
Mots-clés : Systèmes dynamiques, Algorithme d'intégration temporelle explicite et dissipatif, Schéma de Tchamwa–Wielgosz

Laurent Mahéo 1, 2 ; Vincent Grolleau 2, 3 ; Gérard Rio 2

1 Écoles militaires de Saint-Cyr Coëtquidan, laboratoire de mécanique des matériaux, 56381 Guer cedex, France
2 Université de Bretagne-Sud, laboratoire d'ingénierie des matériaux de Bretagne, 56321 Lorient cedex, France
3 École polytechnique, laboratoire de mécanique des solides, 91128 Palaiseau cedex, France
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Laurent Mahéo; Vincent Grolleau; Gérard Rio. Damping efficiency of the Tchamwa–Wielgosz explicit dissipative scheme under instantaneous loading conditions. Comptes Rendus. Mécanique, Volume 337 (2009) no. 11-12, pp. 722-732. doi : 10.1016/j.crme.2009.10.005. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2009.10.005/

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